We analyze the interaction of fermions and bosons through a one-dimensional Yukawa model. We numerically compute the energy eigenstates that represent a physical fermion, which is a superposition of bare fermionic and bosonic eigenstates of the uncoupled Hamiltonian. It turns out that even fast bare fermions require only low-momentum dressing bosons, which attach themselves to the fast fermion through quantum correlations. We compare the space-time evolution of a physical fermion with that of its bare counterpart and show the importance of using dressed observables. The time evolution of the center of mass as well as the wave packet's spatial width suggests that the physical particle has a lower mass than the sum of the masses of its bare constituents. The numerically predicted dressed mass agrees with that from lowest-order perturbation theory as well as with the renormalized mass obtained from the corresponding Feynman graphs. For a given momentum, this lower mass leads to a faster physical particle and a different relativistic spreading behavior of the wave packet.
Wagner, R E.; Ware, M R.; Su, Q; and Grobe, Rainer, "Space-time properties of a boson-dressed fermion for the Yukawa model" (2010). Faculty publications – Physics. 25.